Textbook recommendation on rigorous machine learning results

Question

I am looking for textbook(s) in machine learning theory that satisfies the following:

1. The text should be graduate level. It assumes all undergraduate level mathematics and early graduate level of understanding in probability theory. That is, the reader is assumed to know all undergraduate results and measure theory and (only) basic results in probability theory like laws of large numbers and central limit theorem.
2. The text then builds from the above prerequisite and rigorously presents important results in machine learning theory.
3. If possible, the textbook should not have too much prerequisite in statistics theory.
4. If possible, the textbook should cover some neural network theory.

I am asking for such a textbook because I plan to self-study machine learning theory. I only know as much probability theory as described above and I pretty much know nothing about statistics. I understand that catching up on topics like regression is inevitable. Therefore, in the best scenario, I wish the book covers relevant topics in statistics along with machine learning theory .